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Combining cross-section and time series data is a long and well established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two data sets. We focus on common…

Methodology · Statistics 2022-09-20 Jinyong Hahn , Guido Kuersteiner , Maurizio Mazzocco

We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…

Probability · Mathematics 2019-04-22 Tony Lelievre , Loucas Pillaud-Vivien , Julien Reygner

Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…

Probability · Mathematics 2015-04-29 Farida Kachapova , Ilias Kachapov

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…

Probability · Mathematics 2007-05-23 Magda Peligrad , Sergey Utev

This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…

Statistics Theory · Mathematics 2018-06-06 Ji Hyung Lee , Kyungchul Song

Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…

Statistical Mechanics · Physics 2026-01-16 Gabriel Barreiro , Vladimir Pérez-Veloz

We consider a class of interacting particle systems with values in $[0,\8)^{\zd}$, of which the binary contact path process is an example. For $d \ge 3$ and under a certain square integrability condition on the total number of the…

Probability · Mathematics 2009-06-26 Yukio Nagahata , Nobuo Yoshida

In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…

Probability · Mathematics 2016-08-16 Florence Merlevède , Magda Peligrad , Sergey Utev

We study sufficient conditions for the belonging of random process to certain Besov space and for the Central Limit Theorem (CLT) in these spaces. We investigate also the non-asymptotic tail behavior of normed sums of centered random…

Probability · Mathematics 2015-07-03 E. Ostrovsky , L. Sirota

Drees and Rootz\'en [2010] have proven central limit theorems (CLT) for empirical processes of extreme values cluster functionals built from $\beta$-mixing processes. The problem with this family of $\beta$-mixing processes is that it is…

Probability · Mathematics 2015-11-24 José Gregorio Gómez

In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems…

Probability · Mathematics 2008-12-16 Sophie Dede

In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…

Probability · Mathematics 2017-08-29 Magda Peligrad , Na Zhang

Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…

Mathematical Physics · Physics 2021-03-17 Yu-Chen Cheng , Hong Qian

Under the high-dimensional setting that data dimension and sample size tend to infinity proportionally, we derive the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix. Different…

Statistics Theory · Mathematics 2021-06-21 Liu Zhijun , Bai Zhidong , Hu Jiang , Song Haiyan

M-dependence is a commonly used assumption in the study of dependent sequences. In this paper, central limit theorems for m-dependent random variables under the sub-linear expectations are established based mainly on the conditions of…

Probability · Mathematics 2023-09-12 Wang-Yun Gu , Li-Xin Zhang

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

Dynamical Systems · Mathematics 2018-02-14 Davor Dragicevic , Gary Froyland , Cecilia Gonzalez-Tokman , Sandro Vaienti

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…

Dynamical Systems · Mathematics 2023-07-25 Yeor Hafouta

The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…

Probability · Mathematics 2022-04-08 Conrad J. Burden , Robert C. Griffiths

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of…

Probability · Mathematics 2007-05-23 Greg Anderson , Ofer Zeitouni

We formulate and prove a new sufficient conditions for Central Limit Theorem(CLT) in the space of continuous functions in the terms typical for the approximation theory. We prove that the conditions for continuous CLT obtained by N.C.Jain…

Probability · Mathematics 2013-04-02 E. Ostrovsky , L. Sirota